Maria Balshaw, 54, has been the director of Tate since 2017, the first woman to hold the position. She grew up in Northampton, and after university worked as an academic. In 2002, she switched careers, as the director of Creative Partnerships, a government programme that aimed to develop creativity in young people by bringing schools and artists together. In 2006, she became the director of the Whitworth in Manchester, where she oversaw a building project that doubled its space; in 2011, she took on the role of director of Manchester City Galleries as well. In 2015, she was made a CBE. Her new book, Gathering of Strangers: Why Museums Matter, is based on the lectures she gave in 2022 at Murray Edwards College, Cambridge, when she was Slade professor of fine art.

Did you change your mind about anything while you were working on this book?
Yes. It helped me firm up my thoughts on things where our intention was good, but we didn’t get it right, like the Hogarth show [Hogarth and Europe, in 2022, widely criticised for its disapproving, culture wars tone]. We were too didactic, and we’ve learned from that. I’ve started to understand that the problem with the [museum] paradigm is that you’re supposed to be the authority. Actually, what’s more useful is not to be frightened of your expertise while also accepting that others will want different positions and views, too.

You talk a lot about relevance. Isn’t art sometimes allowed just to be beautiful and life-enriching?
I try not to use the word too much, but museums are tasked with telling history from a modern perspective. We’re shaping stories, and they can either be stories people care about or not. This doesn’t mean you have to lose all sense of joy or fun.

Isn’t there an ever-present danger that galleries end up patronising the very visitors they most long to attract?
When I first went to museums, I found them really intimidating. I look out of this window and I see the steps up to Tate Britain, and I know that historically they’re one of the greatest barriers to entry, because they’re so grand and they speak to a certain kind of cultural privilege. I don’t think you can just leave people to discover Titian. It’s incomprehensible. It’s art with big and difficult themes that tell you it’s important, but you’re not quite sure why.

In the book, you’re critical of the British Museum’s new £50m partnership with BP. Aren’t all museums in the same boat, and simply desperately in need of funds?
I’ve never known a time when we weren’t concerned about funding; that’s a normal part of life as a museum director. Our numbers are not quite back up to where they were pre-pandemic; international tourism is going to take a couple more years to recover, and while local visitors are spending more, that’s against the absolute loss of reserves during Covid, and the effect of inflation on running costs. But the issue the BM faces in taking BP’s money is that the public has moved to a position where they think it is inappropriate, and there’s a dissonance between wishing to be seen as extremely sensitive in the way we relate to other cultures and careful about the resources we consume, and then taking money from a company that has not yet demonstrated whether it’s really committed to changing. The new director of the British Museum [Nicholas Cullinan, late of the National Portrait Gallery] is going to have to deal with a lot of public dismay.

Tell me a bit more about your background, which you describe as working-class.
My dad worked for Northampton borough council – he was head of parks – and my mum was a teacher. I was encouraged to read lots, and I was always taken to the theatre. But the Northampton Museum… I might have gone in once or twice – I was bequeathed a very old doll by my father’s grandmother, and we took it in for them to have a look – but I never really visited because it was not an art museum, and I was interested in art. This is probably grievously unfair but, in my memory, it was very much focused on shoes [Northamptonshire has a long history of shoe-making].

Where were you when you heard you’d been made director of Tate? Did you expect to land the job?
I wasn’t surprised, because you go through such an arduous process. I’d done three interviews. I knew it would be a hard job to get, but I also knew I had deep experience. In Manchester, I’d worked with collections very like the Tate’s. When I heard, I was in Hong Kong. The chair of the trustees rang me. I think he’d forgotten I was there because he called at 3.30 in the morning.

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Were you thrilled?
I was thrilled, and then I was scared, and I think you stay scared. I still come into work feeling terrified. It takes you five or six years just to understand the institution.

Is the museum world sexist?
I think I’ve experienced the same amount of sexism as any woman in a leadership career. Our world certainly isn’t immune to sexism. Of 15 national museums, only two are run by women.

Your clothes are fantastic. Where did you get your wonderful multicoloured coat?
It’s by my friend Duro Olowu, the Nigerian-born British designer. He has a shop in Mason’s Yard [in London] but I can’t really afford him myself, so I got this – as I do all my best clothes – from Vestiare [the secondhand designer fashion site].

What are you most excited about coming up?
In 2025, there will be an Emily Kam Kngwarray exhibition at Tate Modern. She is the most important of the Aboriginal artists who’ve come to global prominence in the last couple of decades. Her extraordinary painting is known a little in this country, but we haven’t seen the best of her work, and her very large-scale abstracts have almost never travelled outside Australia. The work is very political, and utterly beautiful. It will be the most important exhibition Tate has done for a long time. I hope people will come from all over Europe for it, because you’ll never see these great works here again.

And – predictable question! – what’s your favourite piece in the Tate’s collection?
Cornelia Parker’s Cold Dark Matter [an exploded shed, its remnants suspended from the ceiling, made by the British artist in 1991]. It’s absolutely remarkable, full of explosive joy and impossibility. I worked with Connie in Manchester, and we did a Q&A with her, and someone in the audience asked about the explosion. They wanted to know if she’d rehearsed it, and what she would have done if it hadn’t worked. Well, you can’t rehearse an explosion. She said: “I think what I do is paint myself into a corner, and then jump.” So many of my own critical decisions have been made like that. I paint myself into a corner, and then jump.

• Gathering of Strangers: Why Museums Matter (Tate Publishing) is out on 6 June. To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply